Manuscript Oai282-A@1 · Oai282-A.tex · section · 5b6134ec

Channel commutation versus observable locality

Stage 1: local currents, global actions, and bounded locality › Channel commutation versus observable locality · lines 471–486

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The actual En06-A observable-limit theorem requires eventually commuting bounded generators, norm-convergent comparisons, and asymptotic preservation of both cross-products CheungEn06A. Under those requirements,

[a, b] = n lim (j_{n} (a_{n}) j_{n} (b_{n}) - j_{n} (b_{n}) j_{n} (a_{n})) = 0.

Channel commutation alone supplies none of that comparison.

Similarly, common-domain commutation of unbounded fields is not bounded-net causal commutation. The latter is an input in the Family 282 record, not an output of the finite transport ledger.

Displayed formulas in this passage

unlabeled · line 477
$[a, b] = n lim (j_{n} (a_{n}) j_{n} (b_{n}) - j_{n} (b_{n}) j_{n} (a_{n})) = 0.$

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proposition: Proposition: Commuting channels are not an observable-locality theorem